A veteran US law-enforcement official has filed a blockbuster discrimination lawsuit against Homeland Security Secretary Janet Napolitano, charging she pushed him aside to make way for a less-qualified woman who’s “enjoyed a long-standing relationship” with the anti-terror chief.

The lawsuit, which was first reported yesterday by blogger Debbie Schlussel, identifies the woman as Dora Schriro, who was later appointed by Mayor Bloomberg as commissioner of the city Department of Correction, a post she still holds.

The court papers also allege that Suzanne Barr, Napolitano’s chief of staff at Immigration and Customs Enforcement, has engaged in “numerous” acts of “sexually offensive behavior” intended to “humiliate and intimidate male employees.

Barr’s alleged acts include calling one man “in his hotel room and screaming at him that she wanted his ‘c–k in the back of [her] throat.’ ”

The suit was filed by James T. Hayes Jr., special agent in charge of New York City investigations for Immigration and Customs Enforcement.

Hayes, who began his career with the feds as a border patrol agent in 1995, formerly served as director of ICE Detention and Removal Operations in Washington, DC, where he oversaw about 8,500 workers and a $2.5 billion budget.

But Hayes says he was demoted following President Obama’s election and the appointment of Napolitano, a former Arizona governor, to head the Department of Homeland Security.

In court papers filed in Washington federal court, Hayes says Schriro — who previously served as director of the Arizona Department of Corrections under Napolitano — was named a “special adviser” to Napolitano on detention and removal operations in February 2009 and began to replace him at DHS and ICE meetings.

“Schriro was not as qualified for the position plaintiff had because of lack of federal law-enforcement experience,” Hayes’ suit says.

“Schriro did have experience, however, working with Secretary Napolitano. Schriro enjoyed a long-standing relationship with the secretary.”

The suit doesn’t detail the nature of their relationship.

During her 2002 gubernatorial campaign, Napolitano publicly denied rumors that she’s a lesbian. In a 2009 interview, she said, “I just happen not to be married.”

When asked at that time if she was “seeing anybody now,” she answered, “Yes, my staff.”

Hayes’ suit says that when it became clear he was going to be removed from his post, he “felt that he was being targeted because of his gender.”

He charges that in April and May 2009, ICE chief of staff Barr “removed the entire contents of the offices of three male employees, including nameplates, computers and telephones, to the men’s bathroom at ICE headquarters.”

“Barr also created a frat-house type atmosphere that is targeted to humiliate and intimidate male employees,” court papers say.

In addition to the alleged hotel phone call, Barr allegedly “covertly took an ICE BlackBerry device assigned to a male special agent in charge and sent a BlackBerry Messenger message to his female supervisor indicating that the male employee had a crush on the female supervisor and fantasized about her.”

“Further, Barr promoted and otherwise rewarded those male employees who play along with her sexually charged games,” the suit says.

Napolitano hasn’t formally respoded to Hayes’ suit, which was filed in May.

In response to a request for comment from DHS, ICE Director of Public Affairs Brian Hale said, “ICE doesn’t comment on unfounded claims and will respond to Mr. Hayes’ allegations as appropriate through the judicial system.”

Robin Campbell, press secretary for the New York City Department of Correction, said: “Commissioner Schriro’s selection and service at DHS was based on the merits. Any suggestion to the contrary is false.”